Iterative Elimination of Weakly Dominated Strategies in Binary Voting Agendas with Sequential Voting
In finite perfect information extensive (FPIE) games, backward induction (BI) gives rise to all pure-strategy subgame perfect Nash equilibria, and iterative elimination of weakly dominated strategies (IEWDS) may give different outcomes for different orders of elimination. Several conjectures were recently posed in an effort to better understand the relationship between BI and IEWDS in FPIE games. Four of these problems regard binary voting agendas with sequential voting and two alternatives. Those problems are: (1) Assuming no indifferences, is the BI strategy profile, "always vote for my preferred alternative", guaranteed to survive IEWDS using exhaustive elimination? (2) Does any order of IEWDS leave only strategy profiles that generate paths of play consistent with BI? (3) Does there exist an order of IEWDS that leaves only strategy profiles that generate paths of play consistent with BI? (4) Does any order of IEWDS leave at least one strategy profile that generates a path of play consistent with BI? This paper proves all four conjectures. Moreover, the first conjecture is generalized to agendas with indifferences, the second and third conjectures are shown to not hold for binary voting agendas with more than two alternatives, and I comment on additional results related to the last three problems.
I thank the Caltech SURF program for funding and Federico Echenique for advice.
Submitted - sswp1236.pdf